1 Answer

PEPEGA · Answer 1 · 2019-05-26T21:52:37+0000

5) So for parallelogram ABCD, ∠B ≅ ∠D, and ∠A ≅ ∠C. Further, ∠B and ∠A are supplementary (i.e., their sum is 180°), and ∠D and ∠C are also supplementary.

So, we have that m∠B = m∠D. Therefore,

$6x-42=3x+15\\3x=57\\x=19$ .

Now, let's substitute for x back into the expression for either ∠B or ∠D to find it's angle measure.

m∠B =
6(19)-42=72

Now, remember that ∠B or ∠D are supplements of ∠A.

So, m∠B + m∠A = 180°.

That means m∠A = 180° – 72° = 108°.

That seems reasonable, because A appears to be an obtuse angle.

6)

m∠BAE + m∠DAE + m∠ABC = 180°

$3x+6+10x+2+12x-3=180\\25x+5=180\\x=7$

∠ABC ≅ ∠ADC.

m∠ABC =
12(7)-3=81